Scattering of Solitons from the Density Gradient of a Relativistic Bounded Plasma with Variable Streaming

Abstract

We study a relativistic bounded plasma consisting of hot ions and electrons with density gradient and variable streaming. It is observed that the nonlinear wave generated inside is governed by a variable coefficient KdV equation, which we analyse numerically. Furthermore, the solitary wave is scattered at the discontinuity due to inhomogeneity, and the characteristics of the left and right moving wave become different. Such scattering usually takes place in the solar wind, interplanetary shocks, and in the environment of a comet where, as the relativistic effect gives rise to streaming, the non-uniformity of the plasma leads to a density variation. By evaluating a suitable form lof such variations we compute the amplitude, velocity and width of the soliton before and after the scattering. The amplitude of the reflected wave is seen to decrease as in previous observations.